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I know there have been similar questions but I'm still unclear what the overall consensus is. (1) I assumed and have read that photons travel in straight lines unless deflected by gravity but there are conflicting theories. (2) I have heard that single photons takes every possible path but that makes no sense. Why would a single photon traveling from here to the moon go to every other place in the universe along the way. (3) I can understand a single photon traveling as a particle or packet of energy but I have a hard time understanding a single photon traveling as a wave. I have never understood any attempts to answer this. (4) Does a single photon have a frequency and what causes the frequency? If not then how does it have energy? I have many questions about single photons and their frequency.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – David Z Apr 11 '16 at 10:07
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I think CuriousOne's comment provides most of the answers to your question, but for completeness I'll expand it into an answer.

Light is described by quantum field theory and can only be fully understood in this context. We sometimes talk about photons and sometimes talk about light rays, but these are only approximations. As a general principle light behaves like a particle when energy is being exchanged with something else, and like a wave when energy is propagating. So light travels like a wave and interacts like a particle.

Taking your questions in turn:

  1. When we look at light propagating in the classical limit then it travels in straight lines (though these straight lines may appear curved in a curved spacetime).

  2. When we look at light in the quantum regime then the whole concept of a trajectory is meaningless because the trajectory is a classical limit. At quantum scales no particle, including light, has a perfectly defined trajectory. This is why an electron can go through both slits in the Young's slits experiment - because it doesn't have a single perfectly defined trajectory. The calculation of the classical trajectory can be done in various ways, and the Feynmann sum over paths is one approach. This calculation assumes that light simultaneously travels over all possible paths. To what extent this is just a calculational device and to what extent it reflects an underlying physical reality is a matter of opinion.

  3. (and 4) these don't have answers because the questions are based on a misunderstanding of what light is. If you attempted to describe a propagating light ray as photons you would have to use some description like a coherent superposition of many photons.

While it is not the same as a photon, we could think about a light pulse i.e. a short section of a light wave. This is also called a wave packet. Wave packets have an average frequency, but they contain a spread of frequencies so a wave packet does not have a single perfectly defined frequency.

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  • $\begingroup$ anne v, and CuriousOne Thanks for your replies but I still have a hard time with it. I realize this is the overall and overwhelming consensus of the scientific community. But is there not even room to question that. You have to admit a lot of it goes around and around in circles. It sometimes resembles what it may have been like at the end of the Ptolemaic system when the theories became more and more complex in attempts to maintain what I'm sure the most intelligent and certainly the most educated scientist truly believed in. What is wrong with a single and oscillating photon $\endgroup$ – Bill Alsept Apr 8 '16 at 8:09
  • $\begingroup$ what is wrong with the idea of some description like a coherent superposition of many photons? Have you read my idea on my link at the top of my page? Or whats wrong with the idea as Anna put it "a progress of a photon"? I understand the reason for probabilities and wave functions but their not real. Whats wrong with getting back to the reasoning of actual things and causalities etc? I truly am not trying to be argumentative, just very interested. Thanks $\endgroup$ – Bill Alsept Apr 8 '16 at 8:17
  • $\begingroup$ @BillAlsept: There is nothing wrong with you religiously believing in the phlogiston, either, it's just not what we call "mainstream physics". You were asking a question of how a modern physicist explains the "motion of photons" and you got the proper answers that solve all the problems you wanted solved. What is not real about a probability, especially since it describes exactly what is being observed? If you don't believe it, buy yourself a cheap photomultiplier tube and do a few experiments with "photons". $\endgroup$ – CuriousOne Apr 8 '16 at 8:43
  • $\begingroup$ @CuriousOne that my point, no disrespect but to me your ideas to me seem to go in circles. For instance when you talk about using a photomultiplier I'm not sure what to expect? My understanding is that a single photon or small amount of individual photons (physically impact a charged plate which then knock off more photons toward another plate etc. etc. The way you describe it I'm not sure how that would work? Your say no photon travels from A to B, Your saying there some wave that can't be described traveling over there and I guess delivering the photons and there may be other processes. $\endgroup$ – Bill Alsept Apr 8 '16 at 8:55
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    $\begingroup$ @BillAlsept: physicists are generally arch pragamists and the brutal reality is that quantum field theory works. Indeed quantum electrodynamics is the most precisely experimentally tested theory there has ever been. It is tempting to reject theories on the grounds that they are unintuitive, but the lesson of 20th century physics is that intuition is a very poor guide when it comes to physics. $\endgroup$ – John Rennie Apr 8 '16 at 9:13
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Mainstream physics has described the microcosm of molecules, atoms, elementary particles with the theory of quantum mechanics, and in particular the quantum mechanical standard model of elementary particles, and it has a mathematical form, a Lagrangian. . In this Lagrangian the elementary particles, including the photon, are entered as point particles with the mass and quantum numbers shown in the table.

The word "wave" comes in quantum mechanical solutions from the first quantization level. The potential problems at first quantization level are solutions of quantum mechanical equations (Schrodinger, Dirac, Klein-Gordon) where interactions are represented by potentials. These equations are called wave equations because their solutions are sinusoidal functions, and sines and cosines are what describe waves in the macroscopic world, from water waves to sound waves and even to classical electromangetic waves.

The innovation in Quantum Mechanics is that the solutions of these equations are not to be considered trajectory solutions, but are to be complex conjugate squared and the value interpreted as a probability for a particle to be at (x,y,z) at time t. It is an axiom that has been very successful in describing molecules and atoms cf atomic orbitals . In elementary particle interactions the solutions had to be estimated by expansions in pertubative series because of the complexity . This led to the development of the mathematics of second quantization where the solutions for the free QM equations (no potential), the wave functions , are used to build what is called second quantization and quantum field theory, various mathematical formats.

The photon in this framework has its own quantum mechanical equations and its own wavefunction solution. This is a complex wave function and carries the electromagnetic potential information A in complex phases. It can be shown that a classical electromagnetic wave obeying Maxwell's equation emergenes from a confluence of photons with energy h*nu, and nu is the frequency of the macroscopic wave.

So how does the photon move from A to B? It moves with energy=h*nu and velocity c, and carries information about putative electric and magnetic fields of a macroscopic light beam. In first quantization one says that its probability of being at (x,y,z) is the square of the free photon wavefunction which probability does vary with frequency nu.

Photons are usually treated with second quantization, which mathematically assumes that the vacuum is composed by the fields of the elementary particles at a ground state, and creation operator manifests the elementary particle at that point in time.

I have heard that single photons takes every possible path but that makes no sense

You are confusing mathematics with reality, a common enough mistake, (particularly with the concept of virtual particles, but that is another story). The mathematics of calculating the progress of a photon can be formulated in a least action type integral. It does not mean that the photon takes all those paths, as in classical mechanics formulated with the least action, the object does not take all those paths.

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  • $\begingroup$ Creation operators don't create particles but quantum states. A path integral has to be evaluated over all paths to produce the correct result, but it doesn't have to be interpreted as a physical mechanism. Indeed, it should be pretty obvious why that is a bad idea. Quantum fields are not Santa and his sled visiting all chimneys in one night. $\endgroup$ – CuriousOne Apr 8 '16 at 7:48
  • $\begingroup$ @CuriousOne What do you mean with "Creation operators don't create particles"? It certainly changes the expectation value of particle number of a state at least. $\endgroup$ – Mikael Kuisma Apr 8 '16 at 8:05
  • $\begingroup$ @MikaelKuisma: What state a creation operator creates is a matter of mathematical choice. There is no physical content in the structural existence of creation operators. One can not derive the existence of objectifiable "particles" from such a formal tool. Anna, like many other people in hep, has a very old style outlook on these things that stems from a naive understanding of what can be seen in track detectors like bubble chambers. They mistake what they see for objective reality, no matter how little self-consistent sense it makes when one looks at all the evidence. $\endgroup$ – CuriousOne Apr 8 '16 at 8:11
  • $\begingroup$ @CuriousOne I agree, what one should not mix formal theory with interpretation. Particle is more like a concept than a well defined thing anyway. It is used quite freely to describe all kinds of resonances of all kinds of fields. If there is a any perceivable peak in any spectrum, somebody is going to call it a particle :) But regardless, I will still continue to use the concept of a particle in connection with creation operators. (Also, I come from solid state, so I do not know much about QFT. There might be some use of concepts, which do not match perfectly) $\endgroup$ – Mikael Kuisma Apr 8 '16 at 8:17
  • $\begingroup$ @MikaelKuisma: A "particle" is an extremely well defined concept. It is the approximation of the dynamics of an extended body by the dynamics of its center of mass. A "particle" is NOT an object, not even in classical mechanics, it's an approximation procedure that spares us the pain of having to start with continuum mechanics instead of Newton. In QM this procedure stops working completely, which, unfortunately, hasn't stopped plenty of people from making technically 100% false statements about "particles". Particles don't work in solid state physics, either... but OK, if you must. $\endgroup$ – CuriousOne Apr 8 '16 at 8:23

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